The point is, that if you observe ONLY low numbered taxis, over and over, every time you notice a taxi, each time you will be more and more convinced that there are only low-numbered taxis in the town. You have to think that your observations are independent (that is, you don’t count as a separate observation seeing a taxi, glancing to the left, glancing back at the taxi and seeing it again as an independent observation).

Here’s another example, from the first day of class: I had a two headed coin. Suppose I toss a coin 100 times, and every time it comes up heads. Sure, it might be a fair coin, but every time that you toss it and it comes up heads again, you will believe more and more that the coin has two heads (or that I am cheating in some other way).

So, it is reflected in the likelihood by the fact that each observation of the same taxi (or coin toss) will add an additional factor, in the case of taxis, of 1/N, again assuming that the observation events are independent. So if you observe taxi #3, for example, 1000 times, that will be a factor of in the likelihood, which peaks very close to 3.

]]>if you do sample with replacement and you use 1/N^3 as likelihood, I don’t see how seeing for example car 3 1,000 times over and over will affect the likelihood. I understand that Im more sure that there are 3 cars for example, but how is that reflected in the likelihood? is it reflected in the likelihood?. ]]>

Hi Anna, It all depends on how the sampling is done. It’s not so much that you’ve seen it so you know that it exists, it is how you’ve seen it, that is, the sampling scheme.

If there were only one taxi, then you’d always see #1 and never any other number. I’m sure that in that case, if day after day you kept seeing #1 and never any other number, you’d become more and more certain that there was only one taxi.

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